An electronic device makes a deep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 10 a.m. At what time will they beep together at the earliest?

Given: Device 1 beeps after 60 seconds.

Device 2 beeps after 62 seconds.

To find: the time they beep together.

Explanation:

To find the minimum possible value we find LCM.

So, the devices will beep simultaneously at the LCM of intervals of beeps.

So, LCM of 60 and 62 -

Prime factors of the numbers are -

60 = 2 × 2 × 3 × 5

62 = 2 × 31

LCM = product of prime factors with highest powers

= 2² × 3 × 5 × 31

= 1860 seconds

∴ devices will beep simultaneously after 1860 seconds.

We know 1 min = 60 seconds,

So, 1860 seconds = 1860/60 minutes

= 31 minutes.

∴ the next time they will beep simultaneously at 10:31 hrs.